When mesh objects are added together in edit mode to create one single 'object', how can the intersections between the mesh be removed?
I would approach this by using face-select mode, and selecting the visible faces of each constituent element of the model, and assigning the vertices comprising those visible faces to a separate vertex group for each element. If a face is partially visible from the exterior of the mesh, I would assign it to the group. When all of the visible faces of all of the elements have been assigned to vertex groups, hide all of the groups, using the H key. Select the remaining vertices, and delete them, and unhide the vertex groups using ALT-H. Then stitch the constituent elements together.